Contrary to above posting, London City control zone is now Class 'D' full time (24hours a day). If Thames Radar is not working, the controlling authority is Heathrow Approach.
Thames radar usually helpful on allowing zone transits, so long as it does not delay or jeapordise their primary function of EGLC traffic, and IFR traffic to EGKB. It's all a matter of timing to avoid the traffic bulges....